Journal of Symbolic Logic

Computably isometric spaces

Alexander G. Melnikov

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We say that an uncountable metric space is computably categorical if every two computable structures on this space are equivalent up to a computable isometry. We show that Cantor space, the Urysohn space, and every separable Hilbert space are computably categorical, but the space $ \mathcal{C}[0,1]$ of continuous functions on the unit interval with the supremum metric is not. We also characterize computably categorical subspaces of $\mathbb{R}^n$, and give a sufficient condition for a space to be computably categorical. Our interest is motivated by classical and recent results in computable (countable) model theory and computable analysis.

Article information

J. Symbolic Logic, Volume 78, Issue 4 (2013), 1055-1085.

First available in Project Euclid: 5 January 2014

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Zentralblatt MATH identifier

Computable analysis metric space theory


Melnikov, Alexander G. Computably isometric spaces. J. Symbolic Logic 78 (2013), no. 4, 1055--1085. doi:10.2178/jsl.7804030.

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